I: High-dimensionality, Uncertainty Quantification and Scientific Computing, II: Model Reduction for Stochastic Partial Differe

분야Field	2017 Math Colloquium
날짜Date	2017-06-02 ~ 2017-06-02	시간Time	15:50 ~ 18:00
장소Place	Math Sci Bldg 404	초청자Host	-
연사Speaker	Minseok Choi	소속Affiliation	POSTECH
TOPIC	I: High-dimensionality, Uncertainty Quantification and Scientific Computing, II: Model Reduction for Stochastic Partial Differe
소개 및 안내사항Content	part I: High-dimensionality, Uncertainty Quantification and Scientific Computing Abstract: Uncertainty quantification (UQ) has recently gained an increasing amount of attention in scientific computing community and is a fundamental challenge in numerical simulations of many physical/engineering problems. We introduce uncertainty quantification and discuss some of the recently developed UQ methods such as generalized polynomial chaos (gPC) and how to deal with high-dimensional problem inherent in complex problems. part II: Model Reduction for Stochastic Partial Differential Equations Abstract: We present a hybrid methodology for stochastic PDEs based on the dynamically orthogonal (DO) and bi-orthogonal (BO) expansions that provide a low dimensional representation for square integrable random processes. The solution to SPDEs follows the characteristics of KL expansion on-the-fly at any given time. We prove the equivalence of two approaches and provide a unified hybrid framework of those methods by utilizing an invertible and linear transformation between them. We present numerical examples to illustrate the proposed methods, which exhibit exponential convergence comparable with the polynomial chaos (PC) method but with substantially smaller computational cost.

학회명Field	I: High-dimensionality, Uncertainty Quantification and Scientific Computing, II: Model Reduction for Stochastic Partial Differe
날짜Date	2017-06-02 ~ 2017-06-02	시간Time	15:50 ~ 18:00
장소Place	Math Sci Bldg 404	초청자Host	-
소개 및 안내사항Content	part I: High-dimensionality, Uncertainty Quantification and Scientific Computing Abstract: Uncertainty quantification (UQ) has recently gained an increasing amount of attention in scientific computing community and is a fundamental challenge in numerical simulations of many physical/engineering problems. We introduce uncertainty quantification and discuss some of the recently developed UQ methods such as generalized polynomial chaos (gPC) and how to deal with high-dimensional problem inherent in complex problems. part II: Model Reduction for Stochastic Partial Differential Equations Abstract: We present a hybrid methodology for stochastic PDEs based on the dynamically orthogonal (DO) and bi-orthogonal (BO) expansions that provide a low dimensional representation for square integrable random processes. The solution to SPDEs follows the characteristics of KL expansion on-the-fly at any given time. We prove the equivalence of two approaches and provide a unified hybrid framework of those methods by utilizing an invertible and linear transformation between them. We present numerical examples to illustrate the proposed methods, which exhibit exponential convergence comparable with the polynomial chaos (PC) method but with substantially smaller computational cost.

성명Field	I: High-dimensionality, Uncertainty Quantification and Scientific Computing, II: Model Reduction for Stochastic Partial Differe
날짜Date	2017-06-02 ~ 2017-06-02	시간Time	15:50 ~ 18:00
소속Affiliation	POSTECH	초청자Host	-
소개 및 안내사항Content	part I: High-dimensionality, Uncertainty Quantification and Scientific Computing Abstract: Uncertainty quantification (UQ) has recently gained an increasing amount of attention in scientific computing community and is a fundamental challenge in numerical simulations of many physical/engineering problems. We introduce uncertainty quantification and discuss some of the recently developed UQ methods such as generalized polynomial chaos (gPC) and how to deal with high-dimensional problem inherent in complex problems. part II: Model Reduction for Stochastic Partial Differential Equations Abstract: We present a hybrid methodology for stochastic PDEs based on the dynamically orthogonal (DO) and bi-orthogonal (BO) expansions that provide a low dimensional representation for square integrable random processes. The solution to SPDEs follows the characteristics of KL expansion on-the-fly at any given time. We prove the equivalence of two approaches and provide a unified hybrid framework of those methods by utilizing an invertible and linear transformation between them. We present numerical examples to illustrate the proposed methods, which exhibit exponential convergence comparable with the polynomial chaos (PC) method but with substantially smaller computational cost.

성명Field	I: High-dimensionality, Uncertainty Quantification and Scientific Computing, II: Model Reduction for Stochastic Partial Differe
날짜Date	2017-06-02 ~ 2017-06-02	시간Time	15:50 ~ 18:00
호실Host		인원수Affiliation	Minseok Choi
사용목적Affiliation	-	신청방식Host	POSTECH
소개 및 안내사항Content	part I: High-dimensionality, Uncertainty Quantification and Scientific Computing Abstract: Uncertainty quantification (UQ) has recently gained an increasing amount of attention in scientific computing community and is a fundamental challenge in numerical simulations of many physical/engineering problems. We introduce uncertainty quantification and discuss some of the recently developed UQ methods such as generalized polynomial chaos (gPC) and how to deal with high-dimensional problem inherent in complex problems. part II: Model Reduction for Stochastic Partial Differential Equations Abstract: We present a hybrid methodology for stochastic PDEs based on the dynamically orthogonal (DO) and bi-orthogonal (BO) expansions that provide a low dimensional representation for square integrable random processes. The solution to SPDEs follows the characteristics of KL expansion on-the-fly at any given time. We prove the equivalence of two approaches and provide a unified hybrid framework of those methods by utilizing an invertible and linear transformation between them. We present numerical examples to illustrate the proposed methods, which exhibit exponential convergence comparable with the polynomial chaos (PC) method but with substantially smaller computational cost.